- #1

- 713

- 5

## Main Question or Discussion Point

Hello,

I have recently started to study some Geometric Algebra.

I was wondering how should I interpret complex-vectors in [tex]\mathcal{C}^n[/tex] in the framework of Geometric Algebra.

I understand already that a complex-scalar should be interpreted as an entity of the kind:

[tex]z = x + y (\textbf{e}_1 \wedge \textbf{e}_2)[/tex]

where the imaginary-unit is instead the unit bi-vector in [tex]\mathcal{R}^2[/tex]. Now for a real-vector in [tex]\mathcal{R}^n[/tex] one would obviously have:

[tex]\textbf{x} = x_1 \textbf{e}_1 + \ldots + x_n \textbf{e}_n[/tex]

I have recently started to study some Geometric Algebra.

I was wondering how should I interpret complex-vectors in [tex]\mathcal{C}^n[/tex] in the framework of Geometric Algebra.

I understand already that a complex-scalar should be interpreted as an entity of the kind:

[tex]z = x + y (\textbf{e}_1 \wedge \textbf{e}_2)[/tex]

where the imaginary-unit is instead the unit bi-vector in [tex]\mathcal{R}^2[/tex]. Now for a real-vector in [tex]\mathcal{R}^n[/tex] one would obviously have:

[tex]\textbf{x} = x_1 \textbf{e}_1 + \ldots + x_n \textbf{e}_n[/tex]

__But what would be the equivalent if__**x**were instead complex?